Chapter 2: Conversion and Reactor Sizing
Derivation of PBR Reactor Design Equations
\( \frac{dF_{A}}{dW} = r_{A} \)
\( F_{A} = F_{A0} - F_{A0} X \)
\( dF_{A} = 0 - F_{A0} \, dX \)
\( -F_{A0} \frac{dX}{dW} = r_{A} \)
\( F_{A0} \frac{dX}{dW} = -r_{A} \)
\( \frac{F_{A0} \, dX}{-r_{A}} = dW \)
\(\text{at } W = 0, X = 0\)
\( W = F_{A0} \int_{0}^{X} \frac{dX}{-r_{A}} \)